On Well-Founded and Recursive Coalgebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00346322" target="_blank" >RIV/68407700:21230/20:00346322 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/978-3-030-45231-5_2" target="_blank" >https://doi.org/10.1007/978-3-030-45231-5_2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-45231-5_2" target="_blank" >10.1007/978-3-030-45231-5_2</a>

Result language
angličtina
Original language name
On Well-Founded and Recursive Coalgebras
Original language description
This paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive coalgebras for an endofunctor. For monomorphism preserving endofunctors on complete and well-powered categories every coalgebra has a well-founded part, and we provide a new, shorter proof that this is the coreflection in the category of all well-founded coalgebras. We present a new more general proof of Taylor’s General Recursion Theorem that every well-founded coalgebra is recursive, and we study conditions which imply the converse. In addition, we present a new equivalent characterization of well-foundedness: a coalgebra is well-founded iff it admits a coalgebra-to-algebra morphism to the initial algebra.
Czech name
—
Czech description
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Project
<a href="/en/project/GA19-00902S" target="_blank" >GA19-00902S: Injectivity and Monads in Algebra and Topology</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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